Question

[Thu Hien Tran]

B1; Giải các phương trình sau:

a, \(2\sqrt{x+2+2\sqrt{x+1}}-\sqrt{x+1}=4\)

b,\(\sqrt{x}+\sqrt{x+1}=1+\sqrt{x\left(x+1\right)}\)

c,\(x+2\sqrt{7-x}=2\sqrt{x-1}+\sqrt{-x^2+8x-7}+1\)

Answer 1

[svtkvtm]

\(\text{Đ}K:x\ge0;\text{Đ}at:\sqrt{x}=a;\sqrt{x+1}=b\Rightarrow a+b=ab+1\Leftrightarrow ab-a-b+1\Leftrightarrow a\left(b-1\right)-\left(b-1\right)=0\Leftrightarrow\left(a-1\right)\left(b-1\right)=0\Leftrightarrow\left[{}\begin{matrix}a=1\\b=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=0\end{matrix}\right.\left(tm\right)\)